Linear Equations and Graphs

Determining Linear Equations (or Functions) from Information about the Line

If we are given a straight-line graph, we can find the slope m and intercept b by direct measurement, and hence write down the equation. More usually, we are given some information about the line which allows us to calculate m and b and hence write the equation for the line. A linear function can be determined in the following cases:

• Case 1: The slope and a point on the line are known.
• Case 2: Two points on the line are given.

Example 6A.

Case 1: We are given the slope and a point and asked to find the equation of the line:

Example 6B.

Here we look at a special case of the above example where we are given the slope and the x-intercept. As the x-intercept defines a point, we again have the slope of a line and a point on the line and so we can find the linear function.

Note: If we are given the slope and the y-intercept, finding the equation of the line y = mx + b is straighforward as we have both m and b and can substitute these directly into the equation.

Exercise 6.

In the following exercise you are given the slope and one of the following: a general point on the line, the x-intercept or the y-intercept. Use the information given to determine the linear function.

Example 7.

Case 2: We are given two points and asked to find the equation of the line that goes through these two points:

Exercise 7.